Trevor is studying a polynomial function f(x). three given roots of f(x) are –7, 2i, and 7. trevor concludes that f(x) must be a polynomial with degree 3. which statement is true?

trevor is correct.
trevor is not correct because –2i must also be a root.
trevor is not correct there cannot be an odd number of roots.
trevor is not correct because there cannot be both rational and complex roots.

For the polynomial wit hroots -7, 2i and 7 there are two possibilities:

Consider both these cases:

two possible options A and B.

Option B

Trevor isn't correct because -2i must also be a root

Solution:

For the polynomial with roots -7, 2i and 7 their roots can be,

1. ) Real roots

2.) Imaginary roots

The real roots are: -7 and +7

The imaginary root given is: 2i

The imaginary roots come from the square root. So they will be in form of

Therefore,

For f(x) with roots -7 and +7 and we have,

Fundamental Theorem of Algebra states that a polynomial will have exactly as many roots as its degree (the degree is the highest exponent of the polynomial).

So for f(x) with 4 roots, degree of f(x) is 4

So option B is correct. Trevor is not correct because –2i must also be a root.